In the paper, we describe in operator form classes of PDEs that admit PINN's error estimation. Also, for $L^p$ spaces, we obtain a Bramble-Hilbert type lemma that is a tool for PINN's residuals bounding.

翻译：本文以算子形式描述了允许进行物理信息神经网络（PINN）误差估计的偏微分方程类别。此外，针对$L^p$空间，我们获得了一个Bramble-Hilbert型引理，该引理可作为PINN残差界定的工具。